Problem: One day mum asked Petya to sort his toys and get rid of some of them. Petya found a whole box of toy spiders. They were quite dear to him and the boy didn't want to throw them away. Petya conjured a cunning plan: he will glue all the spiders together and attach them to the ceiling. Besides, Petya knows that the lower the spiders will hang, the more mum is going to like it and then she won't throw his favourite toys away. Help Petya carry out the plan.

A spider consists of k beads tied together by k - 1 threads. Each thread connects two different beads, at that any pair of beads that make up a spider is either directly connected by a thread, or is connected via some chain of threads and beads.

Petya may glue spiders together directly gluing their beads. The length of each thread equals 1. The sizes of the beads can be neglected. That's why we can consider that gluing spiders happens by identifying some of the beads (see the picture). Besides, the construction resulting from the gluing process should also represent a spider, that is, it should have the given features. 

After Petya glues all spiders together, he measures the length of the resulting toy. The distance between a pair of beads is identified as the total length of the threads that connect these two beads. The length of the resulting construction is the largest distance between all pairs of beads. Petya wants to make the spider whose length is as much as possible.

<image> <image>

The picture two shows two spiders from the second sample. We can glue to the bead number 2 of the first spider the bead number 1 of the second spider. The threads in the spiders that form the sequence of threads of maximum lengths are highlighted on the picture.

Input

The first input file line contains one integer n (1 ≤ n ≤ 100) — the number of spiders. Next n lines contain the descriptions of each spider: integer ni (2 ≤ ni ≤ 100) — the number of beads, then ni - 1 pairs of numbers denoting the numbers of the beads connected by threads. The beads that make up each spider are numbered from 1 to ni.

Output

Print a single number — the length of the required construction.

Examples

Input

1
3 1 2 2 3


Output

2


Input

2
3 1 2 1 3
4 1 2 2 3 2 4


Output

4


Input

2
5 1 2 2 3 3 4 3 5
7 3 4 1 2 2 4 4 6 2 7 6 5


Output

7

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.util.Comparator;
import java.io.FileOutputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.FileInputStream;
import java.util.NoSuchElementException;
import java.io.Writer;
import java.math.BigInteger;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Nguyen Trung Hieu - vuondenthanhcong11@yahoo.com
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream;
        try {
            inputStream = new FileInputStream("input.txt");
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
        OutputStream outputStream;
        try {
            outputStream = new FileOutputStream("output.txt");
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskF {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int count = in.readInt();
        int answer = 0;
        for (int i = 0; i < count; i++)
            answer += processSpider(in);
        out.printLine(answer);
    }
    private int processSpider(InputReader in) {
        int size = in.readInt();
        int[] from = new int[size - 1];
        int[] to = new int[size - 1];
        IOUtils.readIntArrays(in, from, to);
        for (int i = 0; i < size - 1; i++) {
            from[i]--;
            to[i]--;
        }
        int[][] graph = GraphUtils.buildSimpleGraph(size, from, to);
        int result = 0;
        for (int i = 0; i < size; i++)
            result = Math.max(result, dfs(i, -1, graph));
        return result;
    }

    private int dfs(int vertex, int last, int[][] graph) {
        int result = 0;
        for (int next : graph[vertex]) {
            if (next != last)
                result = Math.max(result, 1 + dfs(next, vertex, graph));
        }
        return result;
    }
}

class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int readInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }

    }

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object...objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    public void printLine(Object...objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

}

class IOUtils {

    public static void readIntArrays(InputReader in, int[]... arrays) {
        for (int i = 0; i < arrays[0].length; i++) {
            for (int j = 0; j < arrays.length; j++)
                arrays[j][i] = in.readInt();
        }
    }

    }

class GraphUtils {
    public static int[][] buildGraph(int vertexCount, int[] from, int[] to) {
        int edgeCount = from.length;
        int[] degree = new int[vertexCount];
        for (int i = 0; i < edgeCount; i++) {
            degree[from[i]]++;
            degree[to[i]]++;
        }
        int[][] graph = new int[vertexCount][];
        for (int i = 0; i < vertexCount; i++)
            graph[i] = new int[degree[i]];
        for (int i = 0; i < edgeCount; i++) {
            graph[from[i]][--degree[from[i]]] = i;
            graph[to[i]][--degree[to[i]]] = i;
        }
        return graph;
    }

    public static int otherVertex(int vertex, int from, int to) {
        return from + to - vertex;
    }

    public static int[][] buildSimpleGraph(int vertexCount, int[] from, int[] to) {
        int[][] graph = buildGraph(vertexCount, from, to);
        simplifyGraph(from, to, graph);
        return graph;
    }

    private static void simplifyGraph(int[] from, int[] to, int[][] graph) {
        for (int i = 0; i < graph.length; i++) {
            for (int j = 0; j < graph[i].length; j++) {
                graph[i][j] = otherVertex(i, from[graph[i][j]], to[graph[i][j]]);
            }
        }
    }

    }